Cyclicly repetitive motion generating system

ABSTRACT

A cyclicly repetitive motion generating system utilizing first and second drive members mounted respectively on first and second spaced axes and including an oscillating member pivotally mounted about the axis of one of said drive members carrying multiple idler means with a continuous loop of flexible drive means in tangential driving engagement with the first and second drive members and in engagement with said idler means, and a link connecting one of said drive members and said oscillating member wherein rotation of the drive members will cause an oscillation of the oscillating member about its axis. The result is a mechanism capable of generating repetitive index cycles consisting of a short dwell, a smooth acceleration to a maximum velocity and a smooth deceleration to a following dwell.

United States Patent [1 1 Brems 1 Jan. 14, 1975 CYCLICLY REPETITIVEMOTION GENERATING SYSTEM [76] Inventor: John Henry Brems, 32867 WhiteOaks Trl., Birmingham, Mich. 48010 [22] Filed: Nov. 2, 1973 21 Appl.No.: 412,469

Primary Examiner-Wesley S. Ratliff, Jr. Attorney, Agent, or Firm-Barnes,Kisselle, Raisch & Choate [57] ABSTRACT A cyclicly repetitive motiongenerating system utilizing first and second drive members mountedrespectively on first and second spaced axes and including anoscillating member pivotally mounted about the axis of one of said drivemembers carrying multiple idler means with a continuous loop of flexibledrive means in tangential driving engagement with the first and seconddrive members and in engagement with said idler means, and a linkconnecting one of said drive members and said oscillating member whereinrotation of the drive members will cause an oscillation of theoscillating member about its axis. The result is a mechanism capable ofgenerating repetitive index cycles consisting of a short dwell, a smoothacceleration to a maximum velocity and a smooth deceleration to afollowing dwell.

20 Claims, 23 Drawing Figures PATENTED JAN] 4 I975 F'Ghl PATENTED3.859.862

sum 2 0? a F'IG.4

CYCLICLY REPETITIVE MOTION GENERATING SYSTEM This invention relates to acyclicly repetitve motion generating system.

Various motion devices which utilize complicated cam grooves andfollowers can accomplish predetermined acceleration, deceleration anddwell and even reversing characteristics; but the cam configurations arevery expensive to build and they admit of no flexibility or adjustmentshort of changing or substituting any particular cam section.

It is an object of the present invention to provide a motion generatingsystem that can be constructed of relatively simple parts in the form ofgears, levers, and chains which can generate repetitive cycles which canrather easily be altered in any portion without expensive machining.

Another object is to provide such a mechanism in which second and thirdharmonics may be readily added to increase the versatility of themechanism.

It is a further object of this invention to provide a mechanism forsuperimposing a reversing motion on a substantially constant motion.

It is another object of this invention to provide a mechanism capable ofgenerating repetitive index cycles consisting of a short dwell, smoothacceleration to a maximum velocity and smooth deceleration to afollowing short dwell.

A still further object of this invention is to provide a mechanismcapable of generating a wide variety of repetitive motion patterns orprofiles.

Other objects and features of this invention relating to the details ofconstruction and operation will be apparent in the following descriptionand claims in which the principles of operation are set forth togetherwith the best modes presently contemplated for the practice of theinvention.

Drawings accompany this disclosure and the various views thereof arebriefly described as:

FIG. 1, a side view of a mechanism for practicing the invention.

FIG. 2, an end view of the mechanism illustrated in FIG. 1 taken on line11.

FIG. 3, a view taken on line 3-3 of FIG. 1.

FIG. 4, a view of the power input taken on line 44 of FIG. 1.

FIGS. 5 to 7, diagrammatic views of the mechanism of FIG. 1 illustratingthe motion.

FIG. 8, a modified mechanism with the addition of a second harmonic.

FIGS. 9, 10, ll illustrate in graph form, respectively, the relativedisplacement, velocity and acceleration which can be obtained by thepreviously illustrated mechanisms. I

FIG. 12, a schematic drawing of the mechanism illustrated in FIG. 8.

FIGS. 13, 14 and illustrate, respectively, in graph form thedisplacement, velocity, and acceleration utilizing a third harmonic.

FIG. 16, a modified mechanism illustrating the addition of two distinctand higher harmonics.

FIGS. 17, l8, l9 illustrate, respectively, in graph form, thedisplacement, velocity and acceleration of a mechanism utilizingmultiple harmonics.

FIG. illustrates an embodiment in which the idler arm pivots about theinput axis.

FIG. 21 illustrates a mechanism similar to that shown in FIG. 20 with asingle higher harmonic added.

FIG. 22, a mechanism for increasing the angle of chain wrap for hightorque applications.

FIG. 23, a modified arrangement for introducing a second or thirdharmonic into the output motion.

Referring to the drawings FIGS. 1, 2, 3 and 4, a frame 2 supports anoutput shaft 4 through bearings 6 and 8. It will be understood that thisoutput shaft in turn drives any one ofa variety of mechanisms, such asan indexing elevator, an indexing conveyor or other type of mechanismrequiring an intermittent indexing rotary drive.

The frame 2 also supports a gear reducer 10 (FIG. 4) driven by asuitable motor 12 through belt 14 and pulleys l6 and 18. The outputshaft 20 of the gear reducer 10 acts as the input shaft of thismechanism. It will be understood that the shaft 20 may be driven by anyone of many other types of input systems, such as a direct drive fromhigh torque prime movers such as air or hydraulic motors, or from somerelated and interconnecting mechanism. The shaft 20 has mounted on it aninput sprocket 22, which is the input member of the mechanism.

An idler arm 24 is mounted to the output shaft 4 through bearings 26 and28. An idler sprocket 30 is mounted to one end of the idler arm 24through shaft 32, bearings 34 and 36 and retainer nuts 38 and 40. Asecond idler sprocket 42 is mounted to the other end of the idler arm 24through shaft 44, bearings 46 and 48 and retainer 50.

An oscillating link 52 is connected at one end to the idler arm 24through shaft 44, bearing 54 and retainer 56. At its other end the link52 is driven by an eccentric shaft 58, bearing 60 and retainer 62 (FIG.3) mounted on the input sprocket 22. The shaft 58 revolves on an axiswhich is eccentric to the axis of the shaft 20.

A flexible drive chain 64 interconnects the input sprocket 22 and anoutput sprocket 66 mounted on the output shaft 4. The chain passes overthe idler sprockets 30 and 42 in completing its driving loop.

If it is hypothetically assumed that the idler arm 24 is maintained in astationary position (as by disconnecting the link 52 from the shaft 54),it can be seen that the input sprocket 22 will drive the output sprocket66 through a ratio determined by the numbers of teeth on the respectivesprockets, and, further, that the speed ratio will be constant.

If it is assumed that the input sprocket 22 is stationary, while theidler arm 24 is moved through some small angle, the output sprocket 66will rotate through some proportional angle.

Therefore, it can qualitatively be seen that if the idler arm 24 isconnected to the eccentric shaft 58 on the input sprocket 22 through thelink 52, that the motion of the output sprocket 66 is the superpositionor summation of motions caused by the rotation of the input sprocket andthe oscillation of the idler arm. Indeed, if the proportions of thesystem are properly chosen, the output sprocket can be made to stopmomentarily or to dwell once during each complete rotation of the inputsprocket.

To construct a viable system based on this concept, it is necessary thatthe chain length remain substantially unaltered over the useful range ofangular positions of the idler arm. How this is accomplished isrepresented schematically in FIG. 5. The output sprocket 66 rotatesabout an axis A, and the input sprocket 22 rotates about an axis A theidler arm 24 also rotates about axis A,; and the idler sprockets 30 and42 rotate about axes A and A, on the idler arm 24. The line of centersfrom A, to A is defined as C, and the line of centers of A, to A isdefined as C If the angle a, between C, and C is chosen such that, atthe approximate center of the oscillation of idler arm 24, the angle ybetween C, and the chain centerline C is 90, and the angle B between C,and the chain centerline C is also 90, then the total developed chainlength will remain substantially constant even through the idler arm 24is rocked about an angle of i 20 about axis A,. The formula for thetotal developed chain length may be developed using straightforwardtrigonometric relationships but becomes extremely long and cumbersome.It has been evaluated with the aid of a computer and the totaldeveloped-length of the chain found to vary less than 1 part in 10,000for a total oscillation angle of i 20. This is negligibly small for allpractical purposes. It should be noted that the pitch diameters of theidler sprockets 30 and 42 need not be identical, nor is it necessarythat the distance from A, to A, be the same as the distance from A, to AThe amplitude and character of oscillation of the idler'arm 24determines the dynamic characteristics of the output sprocket 66. Thequantitative analysis refers to FIGS. 6 and 7 which are the schematickinematic drawings of thesystem. The variables are defined as follows:

rotation of idler arm 24 about axis A,

- I, rotation of output sprocket 66 about axis A,

caused by rotation of idler arm 24 I, rotation of output sprocket 66about axis A,

caused by rotation of input sprocket 22 I total rotation of outputsprocket 66 d) rotation of input sprocket 22 R, pitch radius of outputsprocket R pitch radius of input sprocket R, pitch radius of the arewhich is the envelope of the pitch circle of the idler sprocket duringthe oscillation of the idler arm 24 L, distance from axis A, to pivotconnection of link 52 on arm 24 L eccentric distance from axis A topivot connection of link 52 on input sprocket 22 Referring to FIG. 6which is a schematic drawing showing the rotation of the output sprocket66 due to a rotation of the idler arm 24, assuming the input sprocket 22is stationary, it can be seen that the total rotation of the outputsprocket 66 is caused by two effects. If the idler arm 24 rotatedthrough an angle 0, the output sprocket rotates through that angle 0also, assuming there is no relative movement of the chain between idlersprocket 42 and output sprocket 66. However, there is a movement of thechain shown as S, which in radian measure is The chain length S,subtends an angle on output sprocket 66 equal to S ,/R,

Therefore, the total angle of rotation-of the output sprocket 66 iswhere 9 is the rotation of the idler arm 24.

If we now consider the idler arm 24 stationary, it is easily seen thatthe rotation of the output sprocket 66 due to a rotation of the inputsprocket 22 is Therefore, the total rotation of the output sprocket 66is FIG.. 7 is a schematic drawing relating the rotation, 6, of the idlerarm 24 due to a rotation 0 of the input sprocket 22. The chain andsprocket pitch diameters are omitted for clarity.

It can be seen that if the input sprocket 22 is rotated through an angle4: about axis A the link 52 is moved through a distance S, where S E L,Sin 4) In radian measure Therefore,

0 E (L sin /L,)

Substituting equation (4) in the general relationship established byequation (3), we obtain If it is desired to obtain a cycloidal outputmotion characteristic in which the output sprocket 66 has a momentarydwell once for each revolution of the input sprocket 22, the coefficientof the sin (1) term must be made equal to l, i.e.,

( zl i) 3 R1/R =1 L (L, R )/(R, R,)

Then equation (4) becomes 2/R1) sin which is the classical equation forcycloidal motion.

The relationship between the idler arm angle 0 and the input angle neednot be the simple harmonic established by the crank L as represented byequation (4). It is possible to add a second harmonic to the outputmotion using the technique shown schematically in FIG. 8.

Referring to FIG. 8, the input sprocket 22, output sprocket 66, idlerarm 24, idler sprockets 30 and 42, chain 64 and all their associatedbearings, shafts and retainers remain the same as shown in FIGS. 1, 2, 3and 4. However, the technique for oscillating the idler arm 24 ismodified through the addition of a second harmonic or Fourier component.

A secondary drive sprocket 70 is mounted parallel to and concentric withthe input sprocket 22 on the gear reducer output shaft 20 and bothsprockets rotate with the shaft. An intermediate sprocket 72 is mountedon a suitable shaft and bearings from the frame 2; this intermediatesprocket 72 is driven by sprocket 70 through chain 74. If there aretwice as many teeth on sprocket 70 as on sprocket 72, then sprocket 72will rotate at twice the angular velocity of sprocket 70. An idler link76 is pivotally connected to the sprocket 72 through an eccentric pivot78. The other end of this link 76 is pivotally connected to a primarylink 80 through a shaft 82; and the other end of the link 80 is driventhrough an eccentric shaft 84 on the input sprocket 22.

It can be seen, therefore, that the point 82 on the link 76 makes onevertical oscillation for each revolution of the sprocket 22, and thatthe point 78 on the link 76 makes two vertical oscillations for eachrevolution of the sprocket 22.

A drive link 86 is connected at one end to the idler arm 24 through theshaft 44 and at its other end to the link 76 through a pivot shaft 88.It can be seen, therefore, that the idler arm 24 will make one completeoscillation for each rotation of the input sprocket 22, to which isadded a component of second harmonic whose magnitude is dependent uponthe ratio of the distances along link 76 between points 78, 88 and 82,and the relative eccentricities of shafts 78 and 84 on their respectivesprockets.

The effect of the addition of this second harmonic component may best beillustrated through several examples. In the general case, through anextrapolation of formula 6, it may be hypothesized that the equation ofmotion for the output movement would become:

Note: If F, =l and F 0, we obtain equation (6).

For simplicity, I (R,/R is defined as relative output motion, U, andtherefore:

U=+F,Sin+F sin2 (7) By successive differentiation dU/dd) =1 F, Cos d) 2F Cos 2 d) (Velocity) s dW/ddi F, Sin (b 4 F sin 2 (Acceleration) d UldF, Cos 8 F cos 2 d) (l0) These relationships may now be utilized toestablish the values of F, and F, that best meet the designrequirements, and, subsequently, these values of F, and F will beconverted into usable geometric parameters.

EXAMPLE I thousandth of the total output movement of an index cycle.

With this in mind, we examine the behavior of equation (7), (8), (9),(l0), and (11). It will be noted that when (it 0, then U=d U/d =dU/ d =0for all values of F, and F To achieve the maximum dwell, it is clearthat the velocity, dU/dd), should be set equal to 0; therefore, fromequation (8) Solving equations (12) and (13) for the values of F, and Fthe following are obtained:

Then, for several values of M, the final values of F, and F are asfollows:

Curve in M F, F, FIG. 9, 10, ll

0 l.3333 16667 A, .l l.3667 .18333 A, .2 l .400 .20000 A,,

When these values of F, and F are utilized in equation (7), and thevalues of U calculated for various values of 5, the curves A,, A and Ain FIG. 9 are obtained. It will be noted that the displacement axis isgenerally magnified and further that the output displacement is relativeto a total cyclic displacement of 217. Considering curve A,, it will benoted that the output movement is negative for the first 31 of inputmovement, reaching a value of 0.001 at that point, and then not reaching+0.00l until 42 of input rotation.

Since these curves are symmetrical about the origin, it may be seen thatthe output dwells for 84 (2 X 42) of input rotation if the dwell isdefined as a band whose width is allowed to be i 0.001 X l/2rr X outputangle per index.

It will be further noted that if the definition of dwell width iswidened and M made appropriately larger, the dwell is lengthened interms of input angle. From curve A,, where M 0.2, the total negativemovement is -0.0048 at 42 and crosses +0.0048 at 58, and the total dwellbecomes 116 of input movement if the dwell is a band of output movementequal to $00048 X 1/21r X output angle per index.

i The corresponding velocity and acceleration for an entire half cycleare shown by curve A in FIGS. 10 and 11.

It will be understood that the velocity curves are symmetrical about theline where d) 180 and that the ac.- celeration curves are symmetricalabout the point U 0, d) 180, i.e., the velocity curves remain positivebetween qb 180 and 360, while the acceleration becomes negative orbecomes a deceleration.

The velocityand accceleration scales are relative to an index of Znoutput units per unit of time.

It will be noted that only curve A is presented in FIGS. 10 and 11 sincecurves A and A, would be extremely close to it on the scale used.

EXAMPLE II If it should be desired to make the output velocity as flatas possible near the center of the index stroke, while still retaining adwell of some reasonable value, a different set of conditions must beplaced on equations (7), (8), (9), (10) and (11), as follows:

In order to achieve a dwell at d 0, dU/d O or to widen that dwell dU/dV. Therefore,

1 F, +'F V Defining F] 2 F2 K I In order to achieve a flat velocity at d180, d Uldtb 0, however zFU/dd) at 180 for all values of F, and FTherefore, the next condition may be employed, which is:

Then for several values of K the final values of F, and F, are asfollows:

Curve in K F, F, FIGS. 9, 10. 11

1.00 -.8 .l B, 1.01 .808 .l0l B, 1.02 .8l6 -.l02 B,

When these values of F, and F are utilized in equation (7), and thevalues of U calculated for various values of d), the curves 8,, B and Bin FIG. 9 are obtained. Here again, it is obvious that as thepermissable dwell band width is increased, the total length of dwell interms of input angles is increased.

Curve B, in FIG. represents the relative velocity of the output for astandard output index of 211-, obtained by substituting the value of F,0.8 and F, 0.1 in equation (8). The curves B and B, are omitted in bothFIGS. 9 and 10 because of their near coincidence with curve B,. Itshould be noted that the velocity reaches a maximum of 1.6 and is nearlyconstant over a 709 span of input movement from d) 145 to 215.

Curve B, in FIG. 11 represents the relative acceleration for thesevalues of F, and F when inserted in equation (10).

EXAMPLE Ill If it is desired that the maximum relative velocity,wherever it should be reached during the index cycle, be as low aspossible, a more subtle technique is required. It will also still bedesired to achieve the maximum practical dwell. Therefore, as beforefrom equation (8):

Then set F, N F where N is an unknown parameter, whereupon:

The point of maximum velocity, dU/d wherever it is reached in the cycleoccurs at a point where :PU/driz 0. Substituting equations (16) and and(17) into equation (N and setting it equal to 0.

NK/(N+2) Sin (1) 4K/(N+2) Sin 2 0 which may be solved to yield Cos d)N/8 This establishes a relationship between N and at any point where thevelocity is at an intermediate peak. Equation (18) may then besubstituted back into equawhereupon F, O.I6667K Then for several valuesof K, the final values of F, and F are as follows:

Curves in K F F FIGS. 9.10. H

1.00 .66667 -.l66667 C [.01 .67333 .l6833 C 1.02 .68 .l7 C

When these valuesare utilized in equation (7), and

the values of U calculated for various values of qb, the

EXAMPLE IV In this case, the objectiveisto find those valuesof E and Fwhich achieve the lowest peak acceleration whereverit may occur during acycle while still maintaining amaximum practical dwell. Therefore asbefore from equation (8) And again setting F N F .(N is now a newunknown) Tlhen The point of maximum acceleration, .d Ulddi w'herever itoccurs in the cycle must occur where a' tU/dzp 0. Therefore, equations(16) and (17) are substituted into equation which is then set equal to0.

which reduces to:

This establishes a relationship between N and (b at any point where theacceleration is at an intermediate peak. Equations (22), (16) and (17)may then be substituted into equation (9) to yield a value for themaximum 'velocity at such a point in terms of (i) only which reduces to:

tFV/dd) K [Sin /(l 2 Cos d) Comp/4)] 23) Then for several values of Kthe final values of F, and F are as follows:

Curves in K F F FIGS. '9, l0. ll

[.00 .93333 .0333 D, .01 .94267 .0336 D .02 l952 .034 D As before, thesevalues of F and F are utilized in equations (7.), (8) and (9) tocalculate the curves D,,

D and D in FlGS.9, l0 and 1 As expected, the valueof the peak relativeacceleration is lower than that found in the other curves satisfyingother conditions.

The foregoing examples-are illustrative only to exemplify severalpuremathematical techniques for evaluating thetcoefficients F and F toobtain the desired out- It will now .be shown .how these purecoefficients E and F maybe convertedinto useful dimensionsfor theadditive system shown in F [6.8. FIG. 12 represents the schematicdrawing of the linkage and eccentricities whichcreate'the harmonicsuperposition and establish the relationship between the rotation. 0, ofthe idler arm 24 due to the rotation q) of the input sprocket 22 and therotation 2 of the sprocket 94. The chain and sprocket pitch diametersare omitted for clarity.

It can be seen that if the input sprocket 22 is rotated through an angled) about axis A the link is moved through a distance L Sin ti). lfit istemporarily assumed that pivot 78 is stationary, the resultant movementof link 86 is t/(L4 L5)] 1. Sin (b.

Similarly, Kit is temporarily assumed that the pivot 82 is momentarilystationary while the sprocket 72 rotates through an angle 2 (1) aboutaxis A the resultant movement of link 86 is By superposition, therefore,the total movement of link 86, as represented by the distance S is S E[L /(L L L Sin 4) [L /(L L L Sin This is an approximation which isnearly perfect if the links 80 and 86 are substantially perpendicular tothe link 76.

As Before:

Therefore 6 t/( 4 5) a/ 1)] Sin d i s 4 (L /L,)] Sin 2 (25) Substitutingequation (25) in the general relationship established by equation (3)and simplifying, the following is obtained In a practical application,R,, R R L,, L,,, and L will generally be chosen for mechanicalconvenience; the eccentricities L and L may then be calculated fromthese restatements of (26) and (27).

3 i [R2/(R3 1)l [(L, 5)/ 5] 2 (2 In all four mathematical examples, thevalue for F was always minus, making L positive, so that the directionof L from axis A is as shown in FIG. 12. In the case of L if it ispositive, its direction from A is as shown in FIG. 12; if it isnegative, its direction is 180 opposite from its indicated position inFIG. 12.

While not shown in the examples, a phase shift may be added to thesecond harmonic component to meet those situations where non symmetry ofoutput movement is desired.

Referring again to FIG. 8, if the number of teeth on the sprocket 70 ismade three times as great as the numer of teeth on the sprocket 72, thesprocket 72 will rotate at three times the angular velocity of sprocket70. The motion of the idler arm 24 is now a sum of the fundamental andsome component of third harmonic whose magnitude is dependent upon theratio of the distance along link 76 between points 78, 88 and 82 and therelative eccentricities of shafts 78 and 84 on their respectivesprockets, as was the case with the second harmonic addition.

The effect of the addition of this third harmonic component may againbest be illustrated through several examples. The equation for theoutput motion of the system may now be hypothesized as follows:

U d; F, Sin q) F Sin 3 d) (Displacementhso) By successivedifferentiation:

dU/d= 1 F, Cos 3 F Cos 3 (\(e locity) g3 l) d U/dda F, Sin d) 9 F Sin 3(Acceleration)(32) (WU/dd) F, Cos d1 27 F Cos 3 (33) dU/d i F, Sin 4) 81F Sin 3 34 These relationships may be utilized to establish values of F,and F, that best suit specific design requirements. Several illustrativeexample cases will be outlined.

EXAMPLE V It is desired to design the mechanism to achieve a long dwellusing the third harmonic (rather than the second as in Example I).

By a process completely identical with that used in Example I, it isfound that Then for several values of M, the final values of F, and Fare as follows:

Curves in M F, F, FIGS. l3. l4. l5

0 l.l25 .0416? E .2 -l.l50 .05 E, .4 l.l .05833 B,

When these values are utilized in equation (30), and the value of Ucalculated for various values of (b, the curves [5,, E and E in FIG. 13are obtained. It can be seen that the dwell characteristics so achievedare slightly inferior to those achieved with the second harmonicaddition as shown by curves A,, A and A, in FIG. 9.

Only the curve E is plotted in FIG. 14 from equation (31) representingthe relative velocity using these values of F, and F because of nearidentity of curves E, and E similarly, curve E is plotted alone in FIG.15, from equation (32) representing the relative acceleration usingthese values of F, and F A significant reduction in the values of peakvelocity and peak acceleration will be noted in comparison to the curvesA in FIGS. 10 and 11 which represent the velocity and acceleration formaximum dwell conditions using the second harmonic addition. Therefore,using the third harmonic instead of the second to increase the dwell isa compromise that can be chosen only in the light of a specificapplications requirements.

EXAMPLE VI In this case, it is desired that acceleration be as flat aspossible at an input angle of and that the practical dwell again be aslarge as possible. It is obvious from the form of equation (32) that therelative acceleration must be symmetrical about the line (I: 90; it isfurther obvious that the slope of the acceleration, as expressed byequation (33), is always 0 at d: 90 regardless of the values of F, and FThe curvature of the acceleration is proportional to dU/ddf; therefore,by setting dU/dqb 0 at d) 90 the optimum flatness of the acceleration isachieved; therefore, from equation (32) By again setting the slopeslightly negative at (I: 0, from equation (31) F, +3 F, K Therefore Thenfor several values of K, the final values of F, and F are as follows:

Curves in K F, F, FIGS. 13. 14.15

1.00 -.96429 -.01 1905 G, 1.01 -.97393 .0l2024 G, 1.02 .98357 .0l2l43 G,

flat from d 60 to d) 120 at a value of 0.85, meeting the set-up boundarycondition.

EXAMPLE VII In this case, it is desired that the peak acceleration be aslow as possible wherever it occurs in a cycle and that the practicaldwell again be as large as possible. This situationoccurs when anintermediate peak is reached at some input angle less than 90, and atsome symmetrical angle beyond 90 (due to the aforementioned accelerationsymmetry about 90). It is, therefore, hypothesized that:

F, N F, (where N is again a new unknown) 35 It is also known thatwherever the acceleration is a maximum that d U/dd 0. Therefore, bysubstituting (35) into equation (33), setting equation (33) equal to andclearing, the following is obtained:

Sin 0 27=N/l08 This now establishes a relationship between N and 0 atany point of maximum acceleration. As before, to achieve a slightnegative velocity at (b 0 By combining with equation (35 the followingare obtained:

In order to find at what specific value of N, (dU/dgb has is leastvalue, equation (39) is differentiated with respect to N, and the resultset equal to 0.

After clearing When this is substituted back into equations (37) andThen for several values of K, the final values of F and F are asfollows:

Curves in K F, F; FIGS. l3. l4.

1.00 .9375 -.020833 H, 1.01 -.9469 -.02l04 H, L02 .95625 .02l25 H,

When these values are utilized in equations (30), (31) and (32), and theoutput displacement, velocity,

and acceleration calculated, the curves H,, H, and H, are obtained. InFIG. 15 it will be noted that the acceleration curve B, reaches a peakof0.8l at d) 50 and d) 130, which is some 5 percent less than the moreflattened top of 6,.

Examples V, VI and VII are again intended as illustrative only. Whetherthe value of the factors F, and F 3 are obtained by these methods or byother techniques to meet other requirements, they may again be convertedto usable gometric parameters for the linkage using the methods outlinedabove in connection with the first and second harmonic system.

While the mechanism illustrated in FIG. 8 is capable of superimposingeither a second, third or any other single higher harmonic to theoutput, additional adder links may be added so that multiple higherharmonics may be incorporated into the output characteristics. Theschematic mechanism for adding 2 distinct and separate higher harmonicis shown in FIG. 16.

Referring to FIG. 16, the input sprocket 22, output sprocket 66, idlerarm 24, idler sprockets 30 and 42, chain 64 and all associated bearings,shafts and retainers again remain the same as shown in FIGS. 1, 2, 3 and4, except that the center distance from the output sprocket 66 to theinput sprocket 22 may be increased slightly to provide space for theaddition of multiple additional sprockets, and as will be shown, thetechnique for oscillating the idler arm 24 is again modified.

A secondary drive sprocket and a tertiary drive sprocket 92 are mountedparallel to and concentric with the input sprocket 22 on and to rotatewith the gear reducer output shaft 20. A first intermediate sprocket 94and a second intermediate sprocket 96 are each mounted to the frame 2through suitable shafts and bearings. The sprocket 94 is driven bysprocket 90 through chain 98, and sprocket 96 is driven by sprocket 92through chain 100. As shown in FIG. 16, sprocket 96 rotates at threetimes the angular velocity of the input sprocket 22, and sprocket 94rotates at twice the angular velocity of the input sprocket 22.

A first adder link 102 is pivotally connected to the sprocket 94 throughan eccentric pivot 104. The other end of the link 102 is pivotallyconnected to a primary link 106 through a shaft 108; the other end ofthe link 106 is driven through an eccentric shaft 110 on the inputsprocket 22.

A second adder link 112 is pivotally connected to the sprocket 96through an eccentric pivot 114. The other end of the link 112 ispivotally connected to a secondary link 116 through a shaft 118; theother end of the link 116 is driven through a pivot connection 120 onthe link 102.

A drive link 122 is connected at one end to the idler arm 24 through ashaft 44 and at its other end to the link 112 through a pivot 124.

It can be seen, therefore, that for each revolution of the inputsprocket 22, the idler arm 24 will make one complete oscillation, whichis the summation of a fundamental component dependent on theeccentricity of the pivot 110 on the input sprocket 22, a secondharmonic component dependent on the eccentricity of the pivot 104 on thesprocket 94 and the ratio of the distances between points 104, 120 and108 on the link 102, and a third harmonic component dependent on theeccentricity of the pivot 114 on the sprocket 96 and the ratio of thedistances between points 114, 124 and 118 on the link 112.

"The effect of the addition of second and third harmonic may again bestbe illustrated through several examples. The equation of motion of theoutput movement may now be hypothesized as follows:

U=d +F,Sind +F Sin2+F Sin3 placement) (Dis- By successivedifferentiation:

dU/d =31+ F1 Cos 2F, Cos 2 3 cos 3 (Velocity) d U/d =F, Sin 4F, Sin 2 9Sin 3 (Acceleration) (PU/dd) F, Cos 8F Cos 2 d 27 Cos3(43 (PU/dd) F, Sin(1) +16F Sin 2 81 Sin 3 44 (PU/dd) F, Cos d) 32F Cos 2 (I) 243 Cos 3(1)These relationships may be utilized to meet an extremely wide variety ofrequirements; two examples will be shown.

EXAMPLE VIII It will be further assumed that the maximum dwell will beachieved by requiring that the slope of the acceleration, dU/d at d) 0.Therefore, from equation (43) F, 8F, 27F 0 Since three unknowns, F F andF are to be derived, a third independent relationship between theseunknowns must be established. To do this, equation (45) is utilized withthe stipulation that (PU/dd) H, where H in the physical sense representsthe curvature of the slope of the acceleration, and H becomes thecontrolling parameter of the dwell characteristics. Therefore, fromequation (45),

When equations (46), (47) and (48) are solved, the following values arefound 5 Then, for several values of H, the final values of F,,

F and F are as follows:

* Curves in lo H 1 F F FIGS. 17. 18,19

0 l.5 .3 .0333 J l -l.5417 .3333 .04l7 J 1.5 l.5625 .35 -.0458 J:

When these values are utilized in equation (40), and

the values of U calculated for various values of 4), the curves J J andJ in FIG. 17 are obtained. It will be noted that the dwell can be madeappreciably greater than was possible using only a single harmonicaddition.

Curve .1 in FIGS. 18 and 19 represents the relative velocity andrelative acceleration characteristics under these conditions. Curves Jand J;; are omitted in these two figures because of their near identitywith curve .1

EXAMPLE IX In this example, it is desired that the velocity be asuniform as possible over the center portion of a cycle and that thedwell be as long as possible consistent with this first requirement. Tomeet the latter condition, the dwell effect parameter K is againintroduced into equation (41) at d) 0 whereupon:

In order to achieve the most uniform possible velocity over the centerportion of the cycle, equations (42), (43), (44) and (45) must beexamined at d) 180; at (I) 180, it will be seen that equations (42) and(44), representing [PU/114: and d*U/d 1 O for all values of F1, F2 andF3.

Therefore, the second relationship established to find F F and F is toset (WU/dd) O at d) 180 in equation (43), whereupon F1 '8 F3=O The finalrelationship is established through equation (45). Here it ishypothesized that the curvature of the slope of the dwell, d U/dd asrepresented by factor C should become the controlling parameter;therefore, at d 180 from equation (45):

Solving equations (49), (50) and (51), the following values are found:

F (C- 9 K)/66 F (5C- 12 K)/792 Through numerical representativecalculations for several values of C, an excellent solution of nearperfeet constant velocity over the center of the cycle is foundfor C -1.Therefore, the factors become:

Then, for several values of K, the final values of F F and F- are asfollows:

When these values are utilized in equation (40), the curvesKQK and KinFIG. 17 are obtained, indicating the variation in dwellcharacteristics for the various val ues of K.

Only the curves K are shown in FIGS. 18 and 19 be causeof the nearidentity of curves K and K to K representing the relative velocity andacceleration under these conditions. It will be noted that the relativevelocity is substantially constant at a value of 1.4 from -'=Il5 to dz245, thereby meeting the original design requirements.

The sprocket ratios shown in FIG. 16 are two and three times thefundamental. Any other usable combination'could alsobe used such as 2and 4 or 3 and 5. Furthermore, one or more additional sprockets and Bysuccessive differentiation These relationships may again be utilized tosatisfy many requirements in addition to their usage in the followingexample.

EXAMPLE X The design requirements are the same as those for ExampleVIII, i.e., achieve as long a dwell as possible, but in this instanceusing the third and fifth harmonic in place of the second and third.

By a process completely analogous to that of Example VIII, the followingvalues arefoundfor F F and F F, (H-l-225)/192 Then, for several valuesof H, the final values for F F and F are as follows:

("urves in H F. FIGS. 17. 18. w

0 l.1719 .0651 .004F M 3 -l.1875 .0729 -.0063 M 6 1.2031 .0807 .0078 MWhen these values are utilized in equations (52), (53), and (54), curvesM M and M in FIG. 17 are obtained indicating the dwell characteristics,curve M in FIG. 18 representing the relative velocity characteristicsand curve M in FIG. 19 representing the relative accelerationcharacteristics. It is especially noteworthy that when using the thirdand fifth harmonic, those factors which give the best dwell also providea very flat velocity characteristic through the center portion of thestroke.

In all the foregoing mechanisms, the idler arm was arranged to pivotabout the axis of the output shaft. Under some conditions, it becomesmore convenient to have the idler arm pivot about the input axis as isshown in FIG. 20.

Referring to FIG. 20, an output sprocket rotates about an axis 132 on asuitable shaft mounted in suitable bearings in the frame 2. An inputsprocket 134 is driven by external means about an axis 136 on a suitableshaft. An idler arm 138 is independently mounted to pivot on axis 136.At one end the idler arm 138 has connected to it, through a suitableshaft and bearing, the idler sprocket 140 rotating on an axis 142. Atits other end the idler arm 138 has connected to it through a suitableshaft and bearing another idler sprocket 144 rotating on an axis 146. Adrive chain 148 is in driving engagement with sprocket 134 and sprocket130 and in engagement with the idler sprockets 140 and 144. It can beseen that in the absence of motion of the idler arm 138, the angularvelocity ratio between the input sprocket 134 and the output sprocket130 is the ratio of their pitch diameters.

A link 150 is connected to the input sprocket 134 through a suitableeccentric shaft and bearings on an eccentric axis 152; the other end ofthe link 150 is connected to a beam link 154 through a pivot joint 156at some suitable point along its length. One end of the beam link 154 isconnected to the frame 2 through a suitable shaft and bearings on anaxis 158; the other end of the beam link 154 is pivot connected to adrive link 1150 with a pivot joint 162. The other end of the drive link160 is connected to the idler arm 138 at the pivot joint 146.

It can be seen that as the input sprocket 134 rotates about its axis136, the beam link 154 is caused to oscillate about pivot 158 as drivenby link 150; this in turn causes the idler arm 138 to oscillate aboutaxis 136 as driven by link 160 from beam link 154.

The magnitude of oscillation of the idler arm 138 is determined by theeccentricity of pivot 152 from axis 136, and the ratio of distancesbetween points 158, 156 and 162 on beam link 154. By an analysiscomparable to that employed in the earlier description, it is possibleto show that the motion of the outut sprocket may be made to besubstantially cycloidal through the proper selection of parameters.Therefore, the choice of positioning the idler arm to oscillate on theoutput axis or on the input axis is dependent only on the design factorsof a particular application.

As was the case with the designs with the idler arms oscillating aboutthe output axis, it is equally possible to employ superposition toconstruct Fourier additions when the idler arm is pivoted about theinput axis.

A typical mechanism to add a single higher harmonic is shown in FIG. 21.The basic mechanism is the same as in FIG. 20 with the followingmodifications and additions. A secondary drive sprocket 164 is mountedparallel to and concentric with the input sprocket 134 on the inputshaft. An intermediate sprocket 168 is mounted on a suitable shaft andbearings from the frame 2; this intermediate sprocket 168 is driven bysprocket 164 through chain 170. As shown in FIG. 21, the sprocket 168rotates at twice the angular velocity of sprocket 164 but any othermultiple ratio may be employed.

The beam link 154 is connected to the sprocket 168 through a pivot joint172 which is eccentric to the axis of rotation of the sprocket 168. Itcan be seen, therefore, that a second harmonic is added to the motion oflink 160 and idler arm 138 whose magnitude is determined by theeccentricity of pivot 172 on the sprocket 168 and the ratio of thelengths between points 172, 156 and 162 on the beam link 154.

A second intermediate sprocket and associated linkage may be added justas in the mechanisms in which the idler arm pivoted on the outputsprocket.

In all the cases where the intermediate sprockets are used, it ispossible to apply the input power from some external power source tothat intermediate sprocket, rather than to the input sprocket directly.For example, in FIG. 21, the power may be applied to sprocket 168, inwhich case sprocket 164 is driven through chain 170 and in turn drivessprocket 134 which is the input sprocket of the variable loop.

The system is also available for situations in which the intermediatesprockets are larger than their associated primary sprocket, in whichcase subharmonics are generated. Therefore, a given cycle will notrepeat until the slowest turning of the intermediate sprockets has madeone complete revolution.

The drive link which causes the oscillation of the idler link was, inall cases, shown as being attached to the idler arm on an axis which wascoincident with the axis of one of the idler sprockets. This was donefor mechanical convenience and not kinematic necessity. The link may beattached to the idler arm at any point where an effective torque on theidler arm can be generated about the axis of rotation of the idler arm.

For light duty applications, any or all chain loops in all mechanismsmay be replaced by cogged belts and suitably matching pulleys.

For high torque applications, it may become desirable to increase theangle of chain wrap about the output sprocket. A system foraccomplishing thisis shown schematically in FIG. 22. The input sprocket22 again rotates on the axis A and the output sprocket 66 rotates on theaxis A, as in FIGS. 1 and 5. The idler arm is enlarged to support twoadditional idler sprockets 184 and 186, through suitable shafts andbearings, in addition to the original idler sprockets 30 and 42. Theidler arm 180 is free to pivot on axis A and is oscillated by the link52 from input sprocket 22 as before. The chain 64 passes from inputsprocket 22 to the idler sprocket 30, then to the added idler sprocket186, then to the output sprocket 66, then to the other added idlersprocket 184, then to the idler sprocket 42, and finally back to theinput sprocket 22. It can be seen that the addition of the additionalidler sprockets 184 and 186 significantly increases the angle of chainwrap about the output sprocket 66, and that this addition will have noeffect on the performance of the system if sprockets 30 and 42 arepositioned as earlier described.

It is further evident that a marked increase in wrap may be accomplishedthrough the addition of only one additional idler sprocket, either 184or 186.

This increase in chain wrap around the output sprocket, through theaddition of one or two idler sprocket, is also applicable to all theembodiments in which one or more higher harmonics is added. Furthermore,it may be seen that in those embodiments in which the idler arm 138pivots about the axis A of the input sprocket 134, the angle of chainwrap about that input sprocket 134 may be similarly increased throughthe addition of one or more idler sprockets to the idler arm 138.

Another arrangement for introducing a second or third harmonic into theoutput motion is shown in FIG. 23 (see also FIGS. 1 and 5). As shown,the idler sprocket 42 has one-half the pitch diameter of the inputsprocket 22; therefore, the idler sprocket 42 will make two completerevolutions during the interval that the input sprocket 22 makes onerevolution. It will be noted that the link 52 is no longer attached tothe arm 24 through the shaft 44, but is attached to an eccentric pivotshaft 190 mounted on sprocket 42. This then superimposes a modifiedsecond harmonic component on the motion of the arm 24 and, consequently,to the output motion of the output sprocket 66. The modification of thesecond harmonic arises out of the fact that the sprocket 42 does notrotate at a constant angular velocity about shaft 44 but undergoescyclical velocity changes as arm 24 oscillates about axis A,.

A modified third harmonic may be introduced into the output motion bydesigning the system such that the sprocket 42 is one-third the pitchdiameter of the sprocket 22.

I claim:

1. A multiple step reversible intermittent motion mechanism comprising:

a. a frame,

b. a first drive member rotatably mounted on said frame to rotate on afirst axis,

c. a second drive member rotatably mounted on said frame to rotate abouta second axis spaced from said first axis,

d. an oscillating member pivotally mounted about the axis of one of saiddrive members,

e. multiple idler means mounted on said oscillating member,

f. a continuous loop of flexible drive means in tangential drivingengagement with said first and second drive members and in engagementwith said idler means having a path such that one of said drive membersis external to the topological loop of said flexible drive means andsaid idler means and said other drive member is internal to saidtopological loop,

g. a drive link,

h. means pivotally mounting said drive link at one point to said firstdrive member at an axis spaced from said first axis, and

i. means connecting said link at another point to said oscillatingmember, said other point being spaced from said first point on said linkand spaced from the mounting axis of said oscillating member, whereinrotation of said first drive member will cause an oscillation of saidoscillating member about its mounting axis.

2. A mechanism as defined in claim 1 in which said idler means arepositioned on said oscillating member such that the line of saidflexible drive means from either side of that said drive member withinthe said topological loop of said flexible drive means to the tangencypoint with the first engaged of said multiple idler means, and the linefrom said tangency point to the axis of pivot of said oscillatingmember, form an angle whose mean value during a given oscillation cycleof said oscillating member lies within the range of 70 to 1 3. Amultiple step reversible intermittent motion mechanism comprising:

a. a frame,

b. an output member rotatably mounted on said frame to rotate about afirst axis,

c. an input member rotatably mounted on said frame to rotate about asecond axis spaced from said first axis,

d. an oscillating member pivotally mounted on said first axis,

e. multiple idler means mounted on said oscillating member,

f. a continuous loop of flexible drive means in tangential drivingengagement with said input and output members and in engagement withsaid idler means such that said input member and said idler means liewithin the topological loop of said flexible drive means and said outputmember lies external to the topological loop of said flexible drivemeans,

g. an eccentric drive shaft mounted on said input member, and

h. means connecting said eccentric drive shaft with said oscillatingmember at a point spaced from the mounting axis of said oscillatingmember, wherein rotation of said input member will cause an oscillationof said oscillating member about its mounting axis.

4. A mechanism as defined in claim 3 in which said idler means arepositioned on said oscillating member such that the line of saidflexible drive means from either side of said input member to thetangency point of contact with the first of said idler means, and theline from said tangency point to the axis of pivot of said oscillatingmember form an angle whose mean value during a given oscillation cycleof said oscillating member lies within the range of 70 to 110.

5. A mechanism as defined in claim 3 in which said idler means comprisetwo idler members, with one of said idler members rotatably mounted onone side of said oscillating member with respect to said first axis andthe other of said idler members rotatably mounted on the other side ofsaid oscillating member with respect to said first axis.

6. A mechanism as defined in claim 3 in which said idler means comprisemultiple idler members, with one or more of said idler members rotatablymounted on one side of said oscillating member with respect to saidfirst axis and one or more of said idler members rotatably mounted onthe other side of :said oscillating member with respect to said firstaxis.

7. A mechanism as defined in claim 3 in which said idler means comprisemultiple idler members, with multiple said idler members rotatablymounted on one side of said oscillating member with respect to saidfirst axis and multiple said idler members rotatably mounted on theother side of said oscillating member with respect to said first axis.

8. A mechanism as defined in claim 3 in which said means connecting saideccentric drive shaft with said oscillating member comprises a linkmember rotatably connected at one end to said eccentric shaft androtatably connected at its other end to said oscillating member at apoint spaced from said first axis.

9. A mechanism as defined in claim 3 in which said means connecting saideccentric drive shaft with said oscillating member comprises:

a. an auxiliary drive member rotatably mounted on said frame on an axisspaced from said first axis and said second axis,

b. means driving said auxiliary drive member from said input member,

c. a second eccentric shaft mounted on said auxiliary drive member,

d. a beam link rotatably mounted on said second eccentric shaft,

e. a first link rotatably connected at one end to said first eccentricdrive shaft and. pivotally connected at its other end to said beam linkat a point spaced from said second eccentric shaft, and

f. a second link pivotally connected at one end to said beam link at apoint spaced from said second eccentric shaft and said first linkconnection and pivotally connected at its other end to said oscillatingmember at a point spaced from said first axis.

10. A mechanism as defined in claim 3 in which said means connectingsaid eccentric drive shaft with said oscillating member comprises:

a. multiple auxiliary drive members, each indepen dently and rotatablymounted on said frame on axes spaced from each other and spaced fromsaid first and second axes,

b. multiple means driving said auxiliary drive members at differentangular velocities from said input member,

0. multiple auxiliary eccentric shafts each mounted on one of saidauxiliary drive members,

d. multiple beam links, each rotatably mounted on one of said auxiliaryeccentric shafts,

e. a first link rotatably mounted at one end to said first eccentricdrive shaft and. pivotally connected at its other end to the first ofsaid beam links,

f. connector links, being one less in number than the number of saidbeam links, each pivotally connected at one end to one of said beamlinks and pivotally connected at its other end to another of said beamlinks forming a series of connections from the first of said beam linksto the last of said beam links, and

g. a last link pivotally connected at one end to the last of said beamlinks and pivotally connected at its other end to said oscillatingmember at a point spaced from said first axis.

11. A mechanism as defined in claim 3 in which said means connectingsaid eccentric drive shaft with said oscillating member comprises:

a. a second eccentric shaft mounted on one of said idler means, and

b. a link member rotatably connected at one end to said first eccentricdrive shaft and rotatably connected at its other end to said secondeccentric shaft.

12. A multiple step reversible intermittent motion mechanism comprising:

a. a frame,

b. an output member rotatably mounted on said frame to rotate about afirst axis,

0. an input member rotatably mounted on said frame to rotate about asecond axis spaced from said first axis,

(1. an oscillating member pivotally mounted on said second axis,

e. multiple idler means mounted on said oscillating member,

f. a continuous loop of flexible drive means in tangential drivingengagement with said input and and output members and in engagement withsaid idler means such that said output member and said idler means liewithin the topological loop of said flexible drive means and said inputmember lies external to the topological loop of said flexible drivemeans,

g. an eccentricdrive shaft mounted on said input member, and

h. means connecting said eccentric drive shaft with said oscillatingmember at a point spaced from the mounting axis of said oscillatingmember, wherein rotation of said input member will cause an oscillationof said oscillating member about its mounting axis.

13. A mechanism as defined in claim 12 in which said idler means arepositioned on said oscillating member such that the line of saidflexible drive means from either side of said output member to thetangency point of contact with the first of said idler means and theline from said tangency point to the axis of pivot of said oscillatingmember form an angle whose mean value during a given oscillation cycleof said oscillating member lies within a range of 70 to 1 14. Amechanism as defined in claim 12 in which said idler means comprise twoidler members, with one of said idler members rotatably mounted on oneside of said oscillating member with respect to said second axis and theother of said idler members rotatably mounted on the other side of saidoscillating member with respect to said second axis.

15. A mechanism as defined in claim 12 in which said idler meanscomprise multiple idler members, with one or more of said idler membersrotatably mounted on one side of said oscillating member with respect tosaid second axis and one or more of said idler members rotatably mountedon the other side of said oscillating member with respect to said secondaxis.

16. A mechanism as defined in claim 12 in which said means connectingsaid eccentric shaft with said oscillating member comprises:

a. a beam link pivotally supported from said frame, b. a first linkrotatably connected at one end to said eccentric drive shaft andpivotally connected at its other end to said beam link at a point spacedfrom said frame, and

c. a second link pivotally connected at one point to said beam link at apoint spaced from said frame and pivotally connected at another point tosaid oscillating member, and other point being spaced from said secondaxis.

17. A mechanism as defined in claim 12 in which said eccentric driveshaft with said oscillating member comprises:

a. an auxiliary drive member rotatably mounted on said frame on an axisspaced from said second axis,

b. means driving said auxiliary drive member from said input member,

c. a second eccentric shaft mounted on said auxiliary drive member,

d. a beam link rotatably mounted on said second eccentric shaft,

e. a first link rotatably connected at one point to said first eccentricshaft and pivotally connected at another point to said beam link at apoint spaced from said second eccentric shaft, and

f. a second link pivotally connected at one point to said beam link at apoint spaced from said second eccentric shaft and pivotally connected atanother point spaced from said first point to said oscillating member,said other point being spaced from said second axis.

18. A multiple step reversible intermittent motion mechanism comprising:

a. a frame,

b. a first drive member rotatably mounted on said frame to rotate on afirst axis,

0. a second drive member rotatably mounted on said frame to rotate abouta second axis spaced from said first axis,

d. an oscillating member pivotally mounted about the axis of one of saiddrive members,

e. multiple idler means mounted on said oscillating member,

f. a continuous loop of flexible drive means in tangential drivingengagement with said first and second drive members and in engagementwith said idler means having a path such that one of said drive membersis external to the topological loop of said flexible drive means andsaid idler means and said other drive member is internal to saidtopological loop,

g. an eccentric drive shaft mounted on said first drive member, and

h. means connecting said eccentric drive shaft with said oscillatingmember at a point spaced from the mounting axis of said oscillatingmember, wherein rotation of said first drive member will cause anoscillation of said oscillating member about its mounting axis.

19. A mechanism as defined in claim 18 in which said means connectingsaid eccentric drive shaft with said oscillating member comprises:

a. multiple auxiliary drive members, each independently and rotatablymounted on said frame on axes spaced from each other and spaced fromsaid second axis,

b. multiple means driving said auxiliary drive members at differentangular velocities from one of said drive members,

c. multiple auxiliary eccentric shafts each mounted respectively on oneof said auxiliary drive members,

d. multiple beam links each rotatably mounted on one of said auxiliaryeccentric shafts,

e. a first link rotatably mounted at one end to said first eccentricdrive shaft and pivotally connected at its other end to the first ofsaid beam links,

f. connector links, being one less in number than the number of saidbeam links, each pivotally connected at one end to one of said beamlinks and pivotally connected at its other end to another of said beamlinks forming a series of connections from the first of said beam linksto the last of said beam links, and

g. a last link pivotally connected at one end to the last of said beamlinks and pivotally connected at its other end to said oscillatingmember at a point spaced from said second axis.

20. A mechanism as defined in claim 18 in which said means connectingsaid eccentric drive shaft with said oscillating member comprise:

a. a second eccentric shaft mounted on one of said idler means,

b. a beam link pivotally supported from said frame,

c. a first link rotatably connected at one end to said eccentric driveshaft and pivotally connected at its other end to said beam link at apoint spaced from said frame, and

d. a second link pivotally connected at one end to said beam link at apoint spaced from said frame and rotatably connected at its other end tosaid sec-

1. A multiple step reversible intermittent motion mechanism comprising:a. a frame, b. a first drive member rotatably mounted on said frame torotate on a first axis, c. a second drive member rotatably mounted onsaid frame to rotate about a second axis spaced from said first axis, d.an oscillating member pivotally mounted about the axis of one of saiddrive members, e. multiple idler means mounted on said oscillatingmember, f. a continuous loop of flexible drive means in tangentialdriving engagement with said first and second drive members and inengagement with said idler means having a path such that one of saiddrive members is external to the topological loop of said flexible drivemeans and said idler means and said other drive member is internal tosaid topological loop, g. a drive link, h. means pivotally mounting saiddrive link at one point to said first drive member at an axis spacedfrom said first axis, and i. means connecting said link at another pointto said oscillating member, said other point being spaced from saidfirst point on said link and spaced from the mounting axis of saidoscillating member, wherein rotation of said first drive member willcause an oscillation of said oscillating member about its mounting axis.2. A mechanism as defined in claim 1 in which said idler means arepositioned on said oscillating member such that the line of saidflexible drive means from either side of that said drive member withinthe said topological loop of said flexible drive means to the tangencypoint with the first engaged of said multiple idler means, and the linefrom said tangency point to the axis of pivot of said oscillatingmemBer, form an angle whose mean value during a given oscillation cycleof said oscillating member lies within the range of 70* to 110*.
 3. Amultiple step reversible intermittent motion mechanism comprising: a. aframe, b. an output member rotatably mounted on said frame to rotateabout a first axis, c. an input member rotatably mounted on said frameto rotate about a second axis spaced from said first axis, d. anoscillating member pivotally mounted on said first axis, e. multipleidler means mounted on said oscillating member, f. a continuous loop offlexible drive means in tangential driving engagement with said inputand output members and in engagement with said idler means such thatsaid input member and said idler means lie within the topological loopof said flexible drive means and said output member lies external to thetopological loop of said flexible drive means, g. an eccentric driveshaft mounted on said input member, and h. means connecting saideccentric drive shaft with said oscillating member at a point spacedfrom the mounting axis of said oscillating member, wherein rotation ofsaid input member will cause an oscillation of said oscillating memberabout its mounting axis.
 4. A mechanism as defined in claim 3 in whichsaid idler means are positioned on said oscillating member such that theline of said flexible drive means from either side of said input memberto the tangency point of contact with the first of said idler means, andthe line from said tangency point to the axis of pivot of saidoscillating member, form an angle whose mean value during a givenoscillation cycle of said oscillating member lies within the range of70* to 110*.
 5. A mechanism as defined in claim 3 in which said idlermeans comprise two idler members, with one of said idler membersrotatably mounted on one side of said oscillating member with respect tosaid first axis and the other of said idler members rotatably mounted onthe other side of said oscillating member with respect to said firstaxis.
 6. A mechanism as defined in claim 3 in which said idler meanscomprise multiple idler members, with one or more of said idler membersrotatably mounted on one side of said oscillating member with respect tosaid first axis and one or more of said idler members rotatably mountedon the other side of said oscillating member with respect to said firstaxis.
 7. A mechanism as defined in claim 3 in which said idler meanscomprise multiple idler members, with multiple said idler membersrotatably mounted on one side of said oscillating member with respect tosaid first axis and multiple said idler members rotatably mounted on theother side of said oscillating member with respect to said first axis.8. A mechanism as defined in claim 3 in which said means connecting saideccentric drive shaft with said oscillating member comprises a linkmember rotatably connected at one end to said eccentric shaft androtatably connected at its other end to said oscillating member at apoint spaced from said first axis.
 9. A mechanism as defined in claim 3in which said means connecting said eccentric drive shaft with saidoscillating member comprises: a. an auxiliary drive member rotatablymounted on said frame on an axis spaced from said first axis and saidsecond axis, b. means driving said auxiliary drive member from saidinput member, c. a second eccentric shaft mounted on said auxiliarydrive member, d. a beam link rotatably mounted on said second eccentricshaft, e. a first link rotatably connected at one end to said firsteccentric drive shaft and pivotally connected at its other end to saidbeam link at a point spaced from said second eccentric shaft, and f. asecond link pivotally connected at one end to said beam link at a pointspaced from said second eccentric shaft and said first link connectionand pivotally connected at its other end to said oscillating member at apoint spaced from said first axis.
 10. A mechanism as defined in claim 3in which said means connecting said eccentric drive shaft with saidoscillating member comprises: a. multiple auxiliary drive members, eachindependently and rotatably mounted on said frame on axes spaced fromeach other and spaced from said first and second axes, b. multiple meansdriving said auxiliary drive members at different angular velocitiesfrom said input member, c. multiple auxiliary eccentric shafts eachmounted on one of said auxiliary drive members, d. multiple beam links,each rotatably mounted on one of said auxiliary eccentric shafts, e. afirst link rotatably mounted at one end to said first eccentric driveshaft and pivotally connected at its other end to the first of said beamlinks, f. connector links, being one less in number than the number ofsaid beam links, each pivotally connected at one end to one of said beamlinks and pivotally connected at its other end to another of said beamlinks forming a series of connections from the first of said beam linksto the last of said beam links, and g. a last link pivotally connectedat one end to the last of said beam links and pivotally connected at itsother end to said oscillating member at a point spaced from said firstaxis.
 11. A mechanism as defined in claim 3 in which said meansconnecting said eccentric drive shaft with said oscillating membercomprises: a. a second eccentric shaft mounted on one of said idlermeans, and b. a link member rotatably connected at one end to said firsteccentric drive shaft and rotatably connected at its other end to saidsecond eccentric shaft.
 12. A multiple step reversible intermittentmotion mechanism comprising: a. a frame, b. an output member rotatablymounted on said frame to rotate about a first axis, c. an input memberrotatably mounted on said frame to rotate about a second axis spacedfrom said first axis, d. an oscillating member pivotally mounted on saidsecond axis, e. multiple idler means mounted on said oscillating member,f. a continuous loop of flexible drive means in tangential drivingengagement with said input and and output members and in engagement withsaid idler means such that said output member and said idler means liewithin the topological loop of said flexible drive means and said inputmember lies external to the topological loop of said flexible drivemeans, g. an eccentric drive shaft mounted on said input member, and h.means connecting said eccentric drive shaft with said oscillating memberat a point spaced from the mounting axis of said oscillating member,wherein rotation of said input member will cause an oscillation of saidoscillating member about its mounting axis.
 13. A mechanism as definedin claim 12 in which said idler means are positioned on said oscillatingmember such that the line of said flexible drive means from either sideof said output member to the tangency point of contact with the first ofsaid idler means and the line from said tangency point to the axis ofpivot of said oscillating member form an angle whose mean value during agiven oscillation cycle of said oscillating member lies within a rangeof 70* to 110*.
 14. A mechanism as defined in claim 12 in which saididler means comprise two idler members, with one of said idler membersrotatably mounted on one side of said oscillating member with respect tosaid second axis and the other of said idler members rotatably mountedon the other side of said oscillating member with respect to said secondaxis.
 15. A mechanism as defined in claim 12 in which said idler meanscomprise multiple idler members, with one or more of said idler membersrotatably mounted on one side of said oscillating member with respect tosaid second axis and one or more of said idler members rotatably mountedon the other side of said oscillating member with respect to said sEcondaxis.
 16. A mechanism as defined in claim 12 in which said meansconnecting said eccentric shaft with said oscillating member comprises:a. a beam link pivotally supported from said frame, b. a first linkrotatably connected at one end to said eccentric drive shaft andpivotally connected at its other end to said beam link at a point spacedfrom said frame, and c. a second link pivotally connected at one pointto said beam link at a point spaced from said frame and pivotallyconnected at another point to said oscillating member, and other pointbeing spaced from said second axis.
 17. A mechanism as defined in claim12 in which said eccentric drive shaft with said oscillating membercomprises: a. an auxiliary drive member rotatably mounted on said frameon an axis spaced from said second axis, b. means driving said auxiliarydrive member from said input member, c. a second eccentric shaft mountedon said auxiliary drive member, d. a beam link rotatably mounted on saidsecond eccentric shaft, e. a first link rotatably connected at one pointto said first eccentric shaft and pivotally connected at another pointto said beam link at a point spaced from said second eccentric shaft,and f. a second link pivotally connected at one point to said beam linkat a point spaced from said second eccentric shaft and pivotallyconnected at another point spaced from said first point to saidoscillating member, said other point being spaced from said second axis.18. A multiple step reversible intermittent motion mechanism comprising:a. a frame, b. a first drive member rotatably mounted on said frame torotate on a first axis, c. a second drive member rotatably mounted onsaid frame to rotate about a second axis spaced from said first axis, d.an oscillating member pivotally mounted about the axis of one of saiddrive members, e. multiple idler means mounted on said oscillatingmember, f. a continuous loop of flexible drive means in tangentialdriving engagement with said first and second drive members and inengagement with said idler means having a path such that one of saiddrive members is external to the topological loop of said flexible drivemeans and said idler means and said other drive member is internal tosaid topological loop, g. an eccentric drive shaft mounted on said firstdrive member, and h. means connecting said eccentric drive shaft withsaid oscillating member at a point spaced from the mounting axis of saidoscillating member, wherein rotation of said first drive member willcause an oscillation of said oscillating member about its mounting axis.19. A mechanism as defined in claim 18 in which said means connectingsaid eccentric drive shaft with said oscillating member comprises: a.multiple auxiliary drive members, each independently and rotatablymounted on said frame on axes spaced from each other and spaced fromsaid second axis, b. multiple means driving said auxiliary drive membersat different angular velocities from one of said drive members, c.multiple auxiliary eccentric shafts each mounted respectively on one ofsaid auxiliary drive members, d. multiple beam links each rotatablymounted on one of said auxiliary eccentric shafts, e. a first linkrotatably mounted at one end to said first eccentric drive shaft andpivotally connected at its other end to the first of said beam links, f.connector links, being one less in number than the number of said beamlinks, each pivotally connected at one end to one of said beam links andpivotally connected at its other end to another of said beam linksforming a series of connections from the first of said beam links to thelast of said beam links, and g. a last link pivotally connected at oneend to the last of said beam links and pivotally connected at its otherend to said oscillating member at a point spaced from said second axis.20. A mechanism as defineD in claim 18 in which said means connectingsaid eccentric drive shaft with said oscillating member comprise: a. asecond eccentric shaft mounted on one of said idler means, b. a beamlink pivotally supported from said frame, c. a first link rotatablyconnected at one end to said eccentric drive shaft and pivotallyconnected at its other end to said beam link at a point spaced from saidframe, and d. a second link pivotally connected at one end to said beamlink at a point spaced from said frame and rotatably connected at itsother end to said second eccentric shaft.